Extending the k– ω turbulence model towards oceanic applications

Abstract

Four different two-equation turbulence models for geophysical flows are compared: The k– ϵ model, two new versions of the k– ω model, and the Mellor–Yamada model. An extension of the k– ω model for buoyancy affected and rotating flows is suggested. Model performance is evaluated for a few typical oceanic flows. First, new analytical solutions of the models for the surface layer affected by breaking surface waves are discussed. The deficiencies of earlier attempts are high-lighted, and it is demonstrated why the Mellor–Yamada model and the k– ϵ model fail. It is illustrated that only one version of the k– ω model computes correct decay rates for turbulent quantities under breaking waves. Second, it is demonstrated that all models predict almost identical mixed layer depths and profiles for the turbulent kinetic energy in a classical stratified shear-entrainment experiment if the buoyancy term in the second equation is appropriately weighted. Third, the accuracy and numerical robustness of the new k– ω model in realistic oceanic situations is confirmed by comparison with the data-set of the Ocean Weather Ship ‘Papa’.